Probabilities.InverseGaussianCDFInv Method

Overload List

#SignatureDescription
1procedure InverseGaussianCDFInv(const P: TDenseMtxVec; Mu: Double; Lambda: Double; const Res: TDenseMtxVec);Inverse Gaussian distribution PPF (vectorized).
2function InverseGaussianCDFInv(p: Double; Mu: Double; Lambda: Double): Double;Inverse Gaussian (Wald) percent point function (PPF, quantile / inverse CDF).

Overload 1: procedure InverseGaussianCDFInv(const P: TDenseMtxVec; Mu: Double; Lambda: Double; const Res: TDenseMtxVec);

Inverse Gaussian distribution PPF (vectorized).

#NameDescription
1PDefines distribution probabilities, real vector or matrix with values within closed interval [0,1].
2MuDefines distribution Mu parameter. Mu must be a positive scalar.
3LambdaDefines distribution Lambda parameter. Lambda must be a positive scalar.
4ResAfter calculation stores the PPF calculated from P, Mu and Lambda. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of P.

Result: stored in self (calling object)

Overload 2: function InverseGaussianCDFInv(p: Double; Mu: Double; Lambda: Double): Double;

Inverse Gaussian (Wald) percent point function (PPF, quantile / inverse CDF).

#NameDescription
1pProbability, real value on the closed interval [0,1].
2MuDistribution mean parameter. Mu must be a positive scalar (Mu>0).
3LambdaDistribution shape parameter. Lambda must be a positive scalar (Lambda>0).

Returns: Double - the value x such that InverseGaussianCDF(x,Mu,Lambda)=p. Computed by bisection of the CDF on [SQRTEPS, 1e8]. Probability p must lie on [0,1] and Mu, Lambda must both be positive, otherwise the result is NaN.

Remarks:

The percent point function is the inverse of the cumulative distribution function:

CDFInv(p | mu,lambda) = F^(-1)(p | mu,lambda) where F(x | mu,lambda) = p .

The inverse Gaussian CDF has no simple closed-form inverse; the result is obtained by numerically inverting the CDF with a bisection method (tolerance SQRTEPS). Returns NaN for p outside [0,1], Mu<=0 or Lambda<=0.

See Also: Probabilities.InverseGaussianCDF, Probabilities.InverseGaussianPDF